Coat a 3-quart slow cooker with cooking spray. In a large bowl combine flour, baking powder, sugar, salt, and baking soda. Stir in flax seeds and caraway seeds; set aside.
In a medium bowl whisk together beer, sauerkraut, and mustard. Add beer mixture all at once to flour mixture. Stir just until combined (mixture will be sticky). Spoon batter into prepared slow cooker, pressing batter to edges and smoothing top.
Cover and cook on high-heat setting for 3 to 3-1/2 hours or until a toothpick inserted near the center comes out clean. Turn off slow cooker. Carefully remove lid so condensation from lid does not drip onto bread. Cover opening of slow cooker completely with paper towels; place lid on top. Cool for 10 to 15 minutes. Run a knife around edges of slow cooker; remove bread from cooker. Cool completely on a wire rack.